Prime Factorization Using Quantum Variational Imaginary Time Evolution

TL;DR

This paper proposes a quantum variational imaginary time evolution method for prime factorization, offering an alternative to Shor's algorithm that is more robust to noise and suitable for current quantum hardware.

Contribution

It introduces a novel variational approach using imaginary time evolution to factorize numbers on quantum devices, demonstrating practical implementation on IBMQ hardware.

Findings

Number of circuit evaluations scales as O(n^{5}d)

Successfully factorized numbers using 7-9 qubit Hamiltonians

Demonstrated method's viability on IBMQ Lima hardware

Abstract

The road to computing on quantum devices has been accelerated by the promises that come from using Shor's algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and lack of robust error correction schemes. Here we explore a promising, alternative method for prime factorization that uses well-established techniques from variational imaginary time evolution. We create a Hamiltonian whose ground state encodes the solution to the problem and use variational techniques to evolve a state iteratively towards these prime factors. We show that the number of circuits evaluated in each iteration scales as O(n^{5}d), where n is the bit-length of the number to be factorized and $d$ is the depth of the circuit. We use a single layer of entangling gates to factorize several numbers represented using 7, 8, and 9-qubit Hamiltonians. We also verify the method's performance by implementing it on the IBMQ Lima hardware.